page_title: Multibrot set
section_title: Rendering along the exponent
hierarchical_section_title: Multibrot set / Examples / Rendering along the exponent
caption_attribution_description: English: Multibrot rendered with the real axis as the horizontal and the exponent as the vertical, the imaginary value fixed at zero.
context_page_description: In mathematics, a multibrot set is the set of values in the complex plane whose absolute value remains below some finite value throughout iterations by a member of the general monic univariate polynomial family of recursions. The name is a portmanteau of multiple and Mandelbrot set. The same can be applied to the Julia set, this being called multi-Julia set.
  where d ≥ 2. The exponent d may be further generalized to negative and fractional values.
context_section_description: An alternative method is to render the exponent along the vertical axis. This requires either fixing the real or the imaginary value, and rendering the remaining value along the horizontal axis. The resulting set rises vertically from the origin in a narrow column to infinity. Magnification reveals increasing complexity. The first prominent bump or spike is seen at an exponent of 2, the location of the traditional Mandelbrot set at its cross-section. The third image here renders on a plane that is fixed at a 45-degree angle between the real and imaginary axes.
caption: Multibrot rendered with real value along horizontal axis and exponent along vertical axis, imaginary value fixed at zero
exif: {}